Determining a Sounding Interval Based on Throughput

ABSTRACT

In order to determine a sounding interval, an electronic device iteratively revises a set of potential sounding intervals based on transmission statistics associated with communication of some packets with and other packets without transmission beamforming for the set of potential sounding intervals. In particular, the electronic device calculates rank positions for the set of potential sounding intervals based on an estimated throughput and numbers of packets transmitted with transmission beamforming for the set of potential sounding intervals out of a total number of packets transmitted. Then, the electronic device may determine the output sounding interval based on the ranking. When the convergence criterion is achieved, the electronic device may determine a moment based on calculated frequencies of the rank positions over multiple iterations, which is used to revise the set of potential sounding intervals in the next iteration.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority under 35 U.S.C. 371 to InternationalPatent Application No. PCT/US15/68184, “Determining a Sounding IntervalBased on Throughput,” by Yui Ming Tsang et al., filed on Dec. 30, 2015,which claims priority to U.S. Provisional Patent Application No.62/215,981, “Determining a Sounding Interval Based on Throughput,” byYui Ming Tsang et al., filed on Sep. 9, 2015, the contents of both ofwhich are herein incorporated by reference.

BACKGROUND Field

The described embodiments relate to techniques for wirelesslycommunicating information among electronic devices, includingdetermining a sounding interval for updating transmission beamformingand antenna patterns for wireless communication.

Related Art

Many electronic devices are capable of wirelessly communicating withother electronic devices. For example, these electronic devices caninclude a networking subsystem that implements a network interface for:a cellular network (UMTS, LTE, etc.), a wireless local area network(e.g., a wireless network such as described in the Institute ofElectrical and Electronics Engineers (IEEE) 802.11 standard orBluetooth™ from the Bluetooth Special Interest Group of Kirkland,Wash.), and/or another type of wireless network.

In order to improve performance during wireless communication amongelectronic devices, many electronic devices include multiple antennasthat can use beamforming techniques to provide transmission beamforming.When configured properly, the transmission beamforming can address theperformance challenges in an environment, such as with a multi-pathcommunication channel.

Because the environment of an electronic device can change, it is oftennecessary to update the transmission beamforming. The transmissionbeamforming is usually determined regularly, such as after a timeinterval (which is referred to as a ‘sounding interval’) has elapsed.

However, the choice of the sounding interval represents a tradeoff Ashort sounding interval can provide transmission beamforming that is agood match for the environment (and, thus, may result in a high value ofthe signal-to-noise ratio) at the cost of more overhead. Alternatively,a long sounding interval can reduce the overhead, but may result intransmission beamforming that is less optimal for the environment (and,thus, may result in a lower value of the signal-to-noise ratio). Thedifficulty in selecting the sounding interval and the changes in theenvironment can degrade the performance of the communication.

SUMMARY

The described embodiments relate to an electronic device that determinesa sounding interval. This electronic device includes: an interfacecircuit that, during operation, communicates with one or more otherelectronic devices; a processor; and memory that stores a programmodule, which, during operation, is executed by the processor. Duringoperation, the electronic device initializes a set of potential soundingintervals, where a given potential sounding interval specifies how oftentransmission beamforming is updated using sounding packets. Then, theelectronic device communicates, to at least another electronic devices,some packets with and other packets without transmission beamforming forthe set of potential sounding intervals. During this communication, theelectronic device also updates an antenna pattern. In response, theelectronic device receives transmission statistics for communicationwith the one or more other electronic devices.

The electronic device also calculates rank positions for the set ofpotential sounding intervals based on a performance metric (such as anestimated throughput), which is determined from the transmissionstatistics and numbers of packets transmitted with transmissionbeamforming for the set of potential sounding intervals out of a totalnumber of packets transmitted. Based on the ranking, an output soundinginterval is determined. Next, the electronic device repeats thecommunicating, receiving, and calculating, and calculates frequencies ofthe ranking positions over the iterations and determines the outputsounding interval until a convergence criterion is achieved. When theconvergence criterion is achieved, the electronic device determines amoment based on the calculated frequencies, and revises the set ofpotential sounding intervals based on the determined moment.Furthermore, the electronic device repeats, one or more times, thecommunicating, receiving, calculating the rank positions, determiningthe output sounding interval, calculating the frequencies, anddetermining the moment based on the revised set of potential soundingintervals.

In some embodiments, the electronic device excludes errors in thetransmission statistics that are associated with effects other thantransmission beamforming. Note that the transmission statistics mayinclude one or more of: transmission errors associated with noise,transmission errors associated with collisions and interference, andtransmission errors associated with the antenna pattern.

Moreover, the transmission statistics may include at least two of: thetotal number of packets transmitted, the number of packets transmittedusing transmission beamforming, and a number of packets transmittedwithout using transmission beamforming.

Furthermore, the moment may include a mean and/or a median.

Additionally, the electronic device may include an antenna with multipleelements that, during operation, provides the antenna pattern.

Note that the electronic device may include one of: an access point, anda cellular telephone.

In some embodiments, some or all of the aforementioned operationsperformed by the electronic device are implemented in hardware insteadof the program module.

Another embodiment provides a computer-program product for use with theelectronic device. This computer-program product includes instructionsfor at least some of the operations performed by the electronic device.

Another embodiment provides a method. This method includes at least someof the operations performed by the electronic device.

This Summary is provided merely for purposes of illustrating someexemplary embodiments, so as to provide a basic understanding of someaspects of the subject matter described herein. Accordingly, it will beappreciated that the above-described features are merely examples andshould not be construed to narrow the scope or spirit of the subjectmatter described herein in any way. Other features, aspects, andadvantages of the subject matter described herein will become apparentfrom the following Detailed Description, Figures, and Claims.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a block diagram illustrating electronic devices wirelesslycommunicating in accordance with an embodiment of the presentdisclosure.

FIG. 2 is a flow diagram illustrating a method for determining asounding interval in accordance with an embodiment of the presentdisclosure.

FIG. 3 is a drawing illustrating communication among the electronicdevices in FIG. 1 in accordance with an embodiment of the presentdisclosure.

FIG. 4 is a drawing illustrating interdependent optimizers in one of theelectronic devices in FIG. 1 in accordance with an embodiment of thepresent disclosure.

FIG. 5 is a drawing illustrating the determination of a soundinginterval on a per-client basis in accordance with an embodiment of thepresent disclosure.

FIG. 6 is a block diagram illustrating an electronic device inaccordance with an embodiment of the present disclosure.

Note that like reference numerals refer to corresponding partsthroughout the drawings. Moreover, multiple instances of the same partare designated by a common prefix separated from an instance number by adash.

DETAILED DESCRIPTION

In order to determine a sounding interval, an electronic device mayiteratively revise a set of potential sounding intervals (which specifyhow often transmission beamforming is updated using sounding packets)based on transmission statistics associated with communication of somepackets with and other packets without transmission beamforming for theset of potential sounding intervals. In particular, the electronicdevice may calculate rank positions for the set of potential soundingintervals based on a performance metric (such as an estimatedthroughput), which is determined from the transmission statistics, andnumbers of packets transmitted with transmission beamforming for the setof potential sounding intervals out of a total number of packetstransmitted. (Note that while optimizing the sounding interval, theelectronic device may also update an antenna pattern of the electronicdevice.) Then, the electronic device may determine the output soundinginterval based on the ranking. When the convergence criterion isachieved, the electronic device may determine a moment based on thecalculated frequencies of the rank positions, which is used to revisethe set of potential sounding intervals in the next iteration.

This communication technique may allow the electronic device todynamically determine the largest sounding interval that represents anoptimal tradeoff between overhead and the signal-to-noise ratio.Moreover, the electronic device may be able to dynamically adapt tochanges in a wireless environment, thereby providing improvedcommunication performance. Consequently, the communication technique mayimprove the user experience when using the electronic device.

In the discussion that follows, the electronic device may include aradio that communicates packets in accordance with a communicationprotocol, such as an Institute of Electrical and Electronics Engineers(IEEE) 802.11 standard (which is sometimes referred to as ‘Wi-Fi,’ fromthe Wi-Fi Alliance of Austin, Tex.), Bluetooth (from the BluetoothSpecial Interest Group of Kirkland, Wash.), and/or another type ofwireless interface. In the discussion that follows, Wi-Fi is used as anillustrative example. However, a wide variety of communication protocolsmay be used.

Communication among electronic devices is shown in FIG. 1, whichpresents a block diagram illustrating an access point 110 and electronicdevices 112 (such as a portable electronic device, e.g., a cellulartelephone or a smartphone) wirelessly communicating in an environment108 according to some embodiments. In particular, these electronicdevices may wirelessly communicate while: transmitting advertisingframes on wireless channels, detecting one another by scanning wirelesschannels, establishing connections (for example, by transmittingassociation requests), and/or transmitting and receiving packets (whichmay include the association requests and/or additional information aspayloads).

As described further below with reference to FIG. 6, access point 110and electronic devices 112 may include subsystems, such as a networkingsubsystem, a memory subsystem and a processor subsystem. In addition,access point 110 and electronic devices 112 may include radios 114 inthe networking subsystems. More generally, access point 110 andelectronic devices 112 can include (or can be included within) anyelectronic devices with the networking subsystems that enable accesspoint 110 and electronic devices 112 to wirelessly communicate with eachother. This wireless communication can comprise transmittingadvertisements on wireless channels to enable electronic devices to makeinitial contact or detect each other, followed by exchanging subsequentdata/management frames (such as association requests and responses) toestablish a connection, configure security options (e.g., InternetProtocol Security), transmit and receive packets or frames via theconnection, etc. Note that while instances of radios 114 are shown inaccess point 110 and electronic devices 112, one or more of theseinstances may be different from the other instances of radios 114.

As can be seen in FIG. 1, wireless signals 116 (represented by jaggedlines) are transmitted from radio 114-1 in access point 110. Thesewireless signals 116 may be received by radios 114 in one or more of theother electronic devices 112 (such as electronic device 112-1). Inparticular, access point 110 may transmit packets. In turn, thesepackets may be received by the one or more of electronic devices 112.Moreover, access point 110 may allow electronic devices 112 tocommunicate with other electronic devices, computers and/or servers(such as server 120) via network 118.

Note that the communication between access point 110, electronic device112-1 and/or electronic device 112-2 may be characterized by a varietyof performance metrics, such as: a received signal strength (RSS), adata rate, a data rate for successful communication (which is sometimesreferred to as a ‘throughput’), an error rate (such as a retry or resendrate), a mean-square error of equalized signals relative to anequalization target, intersymbol interference, multipath interference, asignal-to-noise ratio, a width of an eye pattern, a ratio of number ofbytes successfully communicated during a time interval (such as 1-10 s)to an estimated maximum number of bytes that can be communicated in thetime interval (the latter of which is sometimes referred to as the‘capacity’ of a communication channel or link), and/or a ratio of anactual data rate to an estimated data rate (which is sometimes referredto as ‘utilization’).

As discussed further below with reference to FIGS. 2-4, in the disclosedcommunication technique, an interface circuit in an electronic device(such as access point 110) may provide sounding packets to one or moreelectronic devices (such as one or more of electronic devices 112) basedon a sounding interval. Moreover, access point 110 may receivebeamforming information (such as transmission-beamforming information)in response to the sounding packets (e.g., from electronic device 112-1,such as sounding feedback, which is sometimes referred to as ‘compressedbeamforming feedback’ or CBF, or ‘channel-state information’ or CSI),and/or may calculate beam-pattern settings (which is sometimes referredto as an ‘antenna pattern’) for a set of antennas or for elements in anantenna (which are considered equivalent in the present discussion). Forexample, access point 110 may determine amplitudes or weights and phasesfor signals to the set of antennas in access point 110 that providetransmission beamforming (such as via a matrix calculation thatdetermines a steering vector). This transmission beamforming may, on anelectronic device-specific basis, attenuate and/or rotate an antennapattern of access point 110. Alternatively or additionally, the antennapattern may be adapted or changed using pattern shapers (such asreflectors) in an antenna or an antenna element in access point 110,which can be independently and selectively electrically coupled toground to steer the antenna radiation pattern in different directions.Note that the antenna pattern (such as a transmit antenna pattern and/ora receive antenna pattern for use when communicating with a particularelectronic device, such as electronic device 112-1) may be characterizedby a spatially varying intensity, with beams (or local maxima in theintensity) at certain locations or regions, and exclusion zones (withlocal minima in the intensity, e.g., locations or regions having anintensity less than a predefined value) at other locations or regions.

Access point 110 may perform a communication technique to regularlydetermine or adjust the sounding interval that specifies when or howoften the transmission beamforming and/or the antenna pattern areupdated. In particular, the communication technique may determine thesounding interval based on an estimated throughput (and, more generally,one or more performance metrics associated with communication betweenaccess point 110 and electronic device 112-1). For example, the soundinginterval may be selected to maximize the estimated throughput. Note thatthe estimated throughput may be determined based on the physical datarate and the number of packets transmitted.

This communication technique may allow access point 110 to adapt tochanges in its environment and/or changes associated with motion ofelectronic devices 112 (such as electronic device 112-1). Moreover, thecommunication technique may reduce the overhead associated withtransmission of sounding packets. Note that such sounding overhead canbecome dominant when the number of electronic devices in a networkincreases, because the number of packets transmitted per electronicdevice decreases.

In general, the sounding interval is a continuous quantity. Thecommunication technique may provide an approach for obtaining thesounding interval at very high precision, but with very low cost. Thecommunication technique may also provide an approach for detectinginaccurate sounding results to enhance the system stability.Furthermore, the communication technique may be applied to a widevariety of different types of transmission beamforming, such as:

single-user transmission beamforming (Su-TxBF) and a multi-user,multi-input-multi output system (Mu-MIMO) in which the transmissionbeamforming is also performed on a frequency or carrier-specific basis.

In the described embodiments, processing a packet or frame in accesspoint 110 and/or electronic devices 112 includes: receiving wirelesssignals 116 with the packet or frame; decoding/extracting the packet orframe from received wireless signals 116 to acquire the packet or frame;and processing the packet or frame to determine information contained inthe packet or frame (such as feedback about the performance during thecommunication).

Although we describe the network environment shown in FIG. 1 as anexample, in alternative embodiments, different numbers or types ofelectronic devices may be present. For example, some embodimentscomprise more or fewer electronic devices. As another example, inanother embodiment, different electronic devices are transmitting and/orreceiving packets or frames. While FIG. 1 illustrates access point 110performing the communication technique, in some embodiments thecommunication technique is performed by one of electronic devices 112,such as electronic device 112-1.

We now describe embodiments of the method. FIG. 2 is a flow diagramillustrating a method 200 for determining a sounding interval inaccordance with some embodiments, which may be performed by anelectronic device (such as access point 110 or, in other embodiments,one of electronic devices 112 in FIG. 1). During operation, theelectronic device operates with an initial operating condition or O.C.(operation 210), where the initial operating condition includes asounding interval for updating transmission beamforming duringcommunication with another electronic device and an antenna pattern usedwhen communicating with the other electronic device (such as whentransmitting packets to and/or receiving packets from the otherelectronic device).

When a sounding-interval (Si) update criterion (which is sometimesreferred to as a ‘triggering event’) is met (operation 212), theelectronic device initializes a set of potential sounding intervals(operation 214), where a given potential sounding interval specifies howoften transmission beamforming is updated using sounding packets. Then,the electronic device communicates, to at least one or more of the otherelectronic devices, some packets with and other packets withouttransmission beamforming (operation 216) for the set of potentialsounding intervals. (Thus, not every packet is sent with and withouttransmission beamforming. Indeed, a given packet may be set usingtransmission beamforming or without transmission beamforming, i.e., oneor the other. Moreover, the number of packets sent with and the numberof packets sent without transmission beamforming may be different fordifferent potential sounding intervals.) During the communication(operation 216), the electronic device also updates an antenna pattern(operation 218). For example, the electronic device may transmit somepackets using transmission beamforming at different sounding intervalsand with different antenna patterns, and may transmit other packetswithout using transmission beamforming at the different soundingintervals and with the different antenna patterns. In response, theelectronic device receives transmission statistics (operation 220) forcommunication with the one or more other electronic devices.

Moreover, the electronic device calculates rank positions (operation224) for the set of potential sounding intervals based on a performancemetric (such as an estimated throughput), which is determined from thetransmission statistics and numbers of packets transmitted withtransmission beamforming for the set of potential sounding intervals outof a total number of packets transmitted.

Based on the calculated ranking (operation 224), the electronic devicedetermines an output sounding interval (operation 226). Next, theelectronic device repeats (operation 228) the communicating (operation216), updating (operation 218), receiving (operation 220), andcalculating the ranking positions (operation 224), and determines theoutput sounding interval (operation 226) until one or more convergencecriteria are achieved (operation 230). For example, one of theconvergence criteria may be that a difference in the output soundinginterval determined in two or more instances of the repeating (operation226) is less than 1, 3, 5 or 10%. Another non-limiting example criterionis that the confidence internal on the throughput measurement crosses aselected threshold (e.g., 95%).

When the one or more convergence criteria are achieved (operation 230),the electronic device calculates frequencies (operation 232) of theranking positions over the iterations and determines a moment (operation234) based on the calculated frequencies, and revises the set ofpotential sounding intervals (operation 236) based on the determinedmoment. For example, the moment may include a mean and/or a median.

Furthermore, the electronic device repeats (operation 238), one or moretimes, the communicating (operation 216), updating (operation 218),receiving (operation 220), calculating (operation 224), determining(operation 226), calculating (operation 232), and determining (operation234) based on the revised set of potential sounding intervals. Method200 may repeat (operation 238) until a stopping condition (operation240) is achieved. For example, the stopping condition (operation 240)can be: a predetermined number of iterations are performed (such as 10,50 or 100 iterations), a difference in the output sounding intervaldetermined in two or more instances of the repeating (operation 238) isless than 1, 3, 5 or 10% and/or an external signal to stop therecursion. In some embodiments, the stopping condition (operation 240)is a confidence interval (based on an integrated probabilitydistribution function) of at least 75%.

In some embodiments, the electronic device optionally excludes errors(operation 222) in the transmission statistics that are associated witheffects other than transmission beamforming. This is because, ingeneral, transmission beamforming may work best in a cleanradio-frequency environment. Note that the transmission statistics mayinclude one or more of: transmission errors associated with noise,transmission errors associated with collisions and interference, andtransmission errors associated with the antenna pattern.

Moreover, the transmission statistics may include at least two of: thetotal number of packets transmitted, the number of packets transmittedusing transmission beamforming, and a number of packets transmittedwithout using transmission beamforming.

Additionally, the electronic device may include an antenna with multipleelements that, during operation, provides the antenna pattern.

Note that the electronic device may include one of: an access point, anda cellular telephone.

In some embodiments of method 200, there may be additional or feweroperations. Moreover, the order of the operations may be changed, and/ortwo or more operations may be combined into a single operation.

Embodiments of the communication technique are further illustrated inFIG. 3, which presents a drawing illustrating communication among accesspoint 110, electronic device 112-1 and/or electronic device 112-2according to some embodiments. In particular, access point 110 may havean initial operating condition (O.C.) 310, where the initial operatingcondition includes a sounding interval for updating transmissionbeamforming during communication with another electronic device and anantenna pattern used when communicating with the other electronicdevice.

When a sounding-interval (Si) update criterion 312 is met (i.e., thetriggering event), access point 110 may initialize 314 a set ofpotential sounding intervals. Then, access point 110 may communicate, toelectronic device 112-1 and/or electronic device 112-2, packets 316 forthe set of potential sounding intervals, where some of packets 316 useand another portion of packets 316 do not use transmission beamforming.During this communication, access point 110 may update one or moreantenna patterns 318 used with electronic devices 112-1 and 112-2. (Notethat a given antenna pattern in antenna patterns 318 may be associatedwith one or more electronic devices, such as electronic device 112-1.)In response, access point 110 may receive transmission statistics 320for the communication with electronic device 112-1 and/or electronicdevice 112-2. In some embodiments, access point 110 optionally excludeserrors 322 in transmission statistics 320 that are associated witheffects other than transmission beamforming.

Moreover, access point 110 may calculate rank positions 324 for the setof potential sounding intervals based on a performance metric (such asan estimated throughput), which is determined from transmissionstatistics 320, and numbers of packets transmitted with transmissionbeamforming for the set of potential sounding intervals out of a totalnumber of packets transmitted.

Based on the calculated rank positions 324, access point 110 maydetermine an output sounding interval 326. Next, access point 110 mayrepeat the communicating of instances of packets 316, updating the oneor more antenna patterns 318, receiving instances of transmissionstatistics 320, calculating instances of rank positions 324 anddetermining instances of the output sounding interval 326 until aconvergence criterion 328 is achieved.

When convergence criterion 328 is achieved, access point 110 maycalculate frequencies 330 (or probabilities) of rank positions 324 overthe iterations and may determine a moment 332 based on the calculatedfrequencies 330. Moreover, access point 110 may revise 334 the set ofpotential sounding intervals based on the determined moment 332.

Furthermore, access point 110 may repeat, one or more times, thecommunicating of instances of packets 316, updating the one or moreantenna patterns 318, receiving instances of transmission statistics320, calculating instances of rank positions 324, determining instancesof the output sounding interval 326, calculating frequencies 330, anddetermining instances of moment 332 based on the revised 334 set ofpotential sounding intervals until a stopping condition 336 is achieved.

We now describe an exemplary embodiment of the communication technique.In the discussion that follows, transmission beamforming (TxBF) shouldbe understood to be a technique employed in a wireless communicationsystem to combine the signal energy to a desired direction to improvethe link quality of a wireless link and reduce its interfering power toundesired direction(s). Moreover, Su-TxBF is a TxBF technique used whendata is only destined to one station (or receiver). Furthermore, Mu-MIMOis a TxBF technique used when data is destined to more than one station(or receiver) at the same time, and the data can be different acrossstations, which is in contrast with a packet broadcast technique.

In order to enable TxBF, CSI of the channel between a transmitter (Tx)and receiver (Rx) may be needed. CSI may include a set of channelattenuations and phases between each transmit and receive antenna pairfor each frequency subcarrier. The CSI can be obtained implicitly if theuplink and downlink are symmetric or explicitly when it is fed back fromthe receiver. If the CSI is obtained implicitly, it is called ‘implicitsounding,’ while if the CSI is obtained explicitly, it is called‘explicit sounding.’ Additionally, a sounding request may be generatedby the transmitter to inform the parties of interest of its need for themost-updated CSI. If the sounding request is translated to particularsounding packets (such as a null data packet or NDP in an IEEE 802.11standard) as in explicit sounding, the party of interest is the receiverof the link. However, if implicit sounding is employed, the party ofinterest may be the transmitter itself.

Finally, note that a sounding interval may be defined as the timeduration or time interval between two sounding requests.

As noted previously, requesting sounding incurs communication overheadas well as processing overhead. In explicit sounding, a sounding packetis sent from the transmitter and a CSI feedback packet is sent from thereceiver. This typically incurs significant communication cost. On theother hand, in implicit sounding, some digital processing may be neededto form the CSI, which can consume power and introduce delay to thesystem.

In the discussion that follows, explicit sounding is used as anillustrative example. However, the communication technique may also beapplied or used in the case of implicit sounding.

In general, the sounding interval may have three impacts on thethroughput. First, a shorter sounding interval may incur morecommunication overhead. For a system with a large number of stations,each station may only transmit a handful of packets within a soundinginterval. In this case, the communication overhead can become a majorconcern. Second, a long sounding interval may introduce more packeterrors. For example, the CSI can become outdated, and thus may beinvalid for TxBF transmission. A packet transmission using a TxBFtechnique based on invalid CSI may result in packet errors, which willlower the throughput. Third, a wireless communication channel isuncertain in nature. The uncertainty can be due to the noise in thechannel, variations in the capabilities of the transmitters andreceivers, as well as many other random factors (such as collisionsand/or interference in the network). In light of such uncertainty, asounding result (such as the CSI) may not be accurate, which may resultin: a higher-packet error rate; and/or bias in transmission statistics,which can mislead subsequent optimization. By using the communicationtechnique, the electronic device may avoid or reduce adverse effectsassociated with incorrect CSI.

In an exemplary embodiment of the communication technique, throughput(i.e., a data rate for successful communication) is used, at least inpart, as a driving variable for determining the sounding interval forthe electronic device. In general, throughput may provide an aggregatedperformance metric for the effects of various factors that may beimpacted by varying sounding intervals, and may average out the effectsthat do not originate from different sounding intervals (and, thus, maybe suitable for use with wireless-communication environments that arenot very predictable). However, a wide variety of performance metricsmay be used when determining the sounding interval, including: the RSS,the data rate, the error rate (such as the retry or resend rate, or thepacket error rate), the mean-square error of equalized signals relativeto an equalization target, intersymbol interference, multipathinterference, the signal-to-noise ratio, the width of an eye pattern,the ratio of number of bytes successfully communicated during a timeinterval (such as 1-10 s) to the estimated maximum number of bytes thatcan be communicated in the time interval (i.e., the ‘capacity’ of acommunication channel or link), and/or the ratio of the actual data rateto the estimated data rate (i.e., the ‘utilization’).

As shown in FIG. 4, which presents a drawing illustrating interdependentoptimizers in one of the electronic devices in FIG. 1 in accordance withsome embodiments, there may be two interdependent optimizers in thecommunication technique: a rate optimizer 410, and a sounding-intervaloptimizer 412. Note that the two interdependent optimizers may beimplemented using software and/or hardware.

These optimizers may operate cooperatively and may optimize the outcomesiteratively. In particular, rate optimizer 410 and sounding-intervaloptimizer 412 may interact with each other as follows. A determined orselected sounding interval may be input into rate optimizer 410. Then,rate optimizer 410 may determine operating parameters that maximize thethroughput of the electronic device, such as: the modulation level, thebandwidth used and/or whether or not it should use TxBF for the nextpacket transmission.

Rate optimizer 410 may conduct a number of trials. Each trial mayinvolve at least one packet transmission. Moreover, rate optimizer 410may use the feedback from packet transmission to determine whether thechosen operating parameters are suitable.

Then, after a triggering event (such as an elapsed time interval, e.g.,1 s, 5 s, 10 s, 30 s, 1 min, 3 min, etc., or a number of transmittedpackets), rate optimizer 410 may generate transmission statistics forthe trial results (such as a number of packets transmitted with TxBFselected), and may provide the transmission statistics tosounding-interval optimizer 412.

Sounding-interval optimizer 412 may determine a sounding interval (suchas the optimal sounding interval based on the throughput). Inparticular, sounding-interval optimizer 412 may select a set of basicsounding intervals (which are sometimes referred to as a ‘set ofpotential sounding intervals’), e.g., based on the transmissionstatistics. For example, the set of basic sounding intervals mayinclude: 1 μs, 25 μs, 100 μs, and 1000 μs.

Next, sounding-interval optimizer 412 may filter out packet-error eventsdue to non-CSI-error events because these events may adversely affectestimates of the sounding interval. Note that, in general, anon-CSI-error event will impact the packet transmission based on TxBF aswell as non-TxBF. For example, interference from another link may reducethe signal-to-interference-and-noise ratio (SINR) for an arbitrarytransmission. However, the transmission statistics from rate optimizer410 may average out the non-CSI-error event. One performance metric thatcan be used is the throughput generated by TxBF transmission versusnon-TxBF transmission. Another performance metric that can be used iswhether packet transmission in the last or immediately precedinginstance of the transmission statistics is favorable in using TxBF(which is sometimes referred to as a ‘TxBF favorable measure’), and rateoptimizer 410 may attempt to optimize or maximize the TxBF favorablemeasure. This approach may be advantageous because: the number oftransmissions or the duration of the packet transmission may vary ineach instance of the transmission statistics (e.g., because of thenumber of clients in the network and traffic load of the clients); and asuddenly favorable wireless-channel environment may result in a muchhigher throughput even though TxBF is not used in transmission.Consequently, a normalization technique may be needed across differentinstances of the transmission statistics.

However, it may be costly and/or difficult to obtain a normalized valuefor different instances of the transmission statistics if the throughputor another aggregated value is used. For example, one approach forobtaining a normalized value is to determine the total number of packettransmissions or total throughputs in the last several instances of thetransmission statistics. This approach may require that the aggregatedvalues from each of the instances of the transmission statistics bestored in memory. Given that a desired sounding interval can be at mostseveral seconds while a packet transmission can take as little as 10 μs,the memory needed may be quite significant.

Using a performance metric that is related to the TxBF favorable measuremay be simpler and less costly. In particular, the TxBF favorablemeasure may include one bit of information from each of the instances ofthe transmission statistics. Moreover, the TxBF favorable measure mayfilter out variation in the throughput associated with variations intraffic load and environment.

Thus, for each sounding interval, the electronic device may store orinclude the number of times TxBF is favorable in the transmissionstatistics and the total number of instances of the transmissionstatistics that were received. For example, during a particulartransmission, TxBF may be considered ‘favorable’ if it yields thehighest throughput (or the highest estimated throughput) for a givenmodulation and coding scheme. In contrast, other types of errors (suchas those due to noise, collisions or interference) may have similarpacket errors rates for TxBF and non-TxBF, and therefore theirthroughputs are proportional to the modulation and coding scheme used(which can be used by sounding-interval optimizer 412 to filter outpacket-error events due to non-CSI-error events).

In some embodiments, a technique such as the binomial confidenceinterval or the Chernoff bound is used to generalize the probability ofTxBF being favorable. However, more generally a wide variety oftechniques may be used. In particular, such techniques may be used toextrapolate results to a larger sample size.

When rate optimizer 410 requests a new sounding interval,sounding-interval optimizer 412 may determine or select one based on thegeneralized performance metric.

Note that the frequency of requests for a new sounding interval can betime-based and/or packet-based. In a time-based approach, the requestmay be made after a time interval has elapsed (such as 30 s, 1 min, 3min, 5 min, 10 min, 15 min, 30 min or an hour). Alternatively oradditionally, for a packet-based approach, the request may be made aftera number of packets have been sent (such as 10, 100, 500 or 1000packets).

In some embodiments, the recorded numbers used in the communicationtechnique are aged appropriately after some duration (such as 30 s, 1min, 3 min, 5 min, 10 min, 15 min, 30 min or an hour), so more-recent orfresher measurements are used to determine the sounding interval.

Furthermore, the set of basic sounding intervals may be discrete.However, the precision may not be high enough. In order to increase theprecision of the sounding interval, an iterative procedure may be used.In particular, given a set of basic sounding intervals, the electronicdevice may record or determine the number of times a given basicsounding interval is chosen at each sounding interval requested by rateoptimizer 410.

Then, at a triggering event, the electronic device may declare an end ofa stage and may calculate the percentage of the time each basic soundinginterval was determined. Note that the triggering event can betime-based (such as after a timing threshold or after a time intervalhas elapsed), input-based (i.e., after a number of inputs, such as anumber of sounding intervals) and/or output-based (i.e., after a numberof output requests). For example, the time interval may be: 30 s, 1 min,3 min, 5 min, 10 min, 15 min, 30 min or an hour. Alternatively, thenumber of inputs or the number of output requests may be: 10, 100, 500or 1000.

Using this percentage or frequency, the electronic device can calculatea new sounding interval based on a linear combination of the basicsounding intervals in the set of basic sounding intervals and theirassociated percentages or frequencies. This new sounding interval issometimes referred to as a ‘derived sounding interval.’ This approachmay allow the new sounding interval to be determined by interpolatingbetween the discrete set of basic sounding intervals.

In some embodiments, the derived sounding interval is determined bycalculating frequencies of rank positions for the set of basic soundingintervals based on an estimated throughput for the numbers of packetstransmitted with TxBF for different basic sounding intervals out of atotal number of packets transmitted (e.g., the number of times when TxBFis favorable, such as based on the estimated throughput, at the timewhen the sounding interval optimizer receives transmission statisticsfrom the rate optimizer). For example, the frequencies may indicate howoften a particular basic sounding interval is at the top of the ranking.Then, the derived sounding interval may be determined by computing amoment based on the calculated frequencies of the different basicsounding intervals in the set of basic sounding intervals. Inparticular, the moment may include the mean or the median. In this way,the electronic device may interpolate among the discrete soundingintervals in the set of basic sounding intervals.

In an exemplary embodiment, the estimated throughput is determined basedon a physical data rate and the number of packets transmitted with TxBFout of a total number of packets transmitted for different basicsounding intervals. Then, basic sounding intervals are ranked relativeto each other based on the associated ratios. These operations may berepeated multiple times to determine the frequencies of the rankpositions (such as, for a given basic sounding interval, a 1^(st) rankposition 25% of the time, a 2^(nd) rank position 15% of the time, etc.)for the different basic sounding intervals. In general, the soundinginterval may be the largest value that maximizes the rank position themost often. However, this is a discrete approach for determining thesounding interval. Instead, in some embodiments the derived soundinginterval is determined by calculating the moment (such as the mean orthe median) using the rank positions and the associated frequencies forthe different basic sounding intervals. For example, a first soundinginterval may have the 1^(st) rank position 25% of the time, a secondsounding interval may have the 1^(st) rank position 15% of the time,etc. In this way, the derived sounding interval may be weighted by thebasic sounding intervals that produce the best throughput (the highestratio for using TxBF or without using TxBF the most often).

After calculating the derived sounding interval, there may be N+1sounding intervals. The electronic device may repeat at least some ofthe operations in the communication technique, but now the calculationof the next instance of the derived sounding interval may be based onbasic sounding intervals and the previous instance of the derivedsounding interval. In this way, the derived sounding interval may beiteratively or dynamically updated.

Ideally, after several iterations the derived sounding interval is anoptimal one. More generally, the communication technique may be iterateduntil a convergence criterion is achieved, such as when a differencebetween the next instance of the derived sounding interval and anaverage of one or more of the previous instances of the derived soundinginterval is less than 1, 3, 5 or 10% or when a confidence interval is atleast 75%.

In an exemplary embodiment, while determining the sounding interval, theelectronic device may update an antenna pattern that is used duringtransmission and/or receiving. For example, as shown in FIG. 5, on a perclient basis, the electronic device may determine rankings based ontransmission statistics for multiple predefined antenna patterns 510 atdifferent sounding intervals 512. Although described as having twoantenna patterns, there may be any number of antenna patterns. Moreover,Antenna patterns may be formed by shaping a radiation pattern from aradiating element by, for example, enabling and/or disabling reflectorsand/or directors associated with a radiating element. In particular, theelectronic device may tabulate a frequency of the top rank position of aperformance metric, such as an estimated throughput (although, one ormore other performance metrics may be used), for each of predefinedantenna patterns 510 at each of the sounding intervals 512. Moreover,this tabulation may be performed for those packets communicated usingtransmission beamforming 514 and those packets communicated withouttransmission beamforming 516 at the different sounding intervals 512.

Then, the probability distribution for the throughput-based frequencyrankings may be integrated to determine the cumulative distributionfunction. This cumulative distribution function may be used to selectthe sounding interval and the predefined antenna pattern with thehighest throughput having a confidence interval that exceeds a thresholdvalue (such as 50% or 75%). In general, for two or more soundingintervals having the same throughput and confidence interval, theelectronic device will select the longest sounding interval as thesounding interval.

In some embodiments, during the communication technique, packets (whichmay be packets transmitted the normal course of operation or may bespecial types of packets) in a queue are transmitted using TxBF with asounding interval of 50 ms and then 100 ms. The estimated throughput,respectively, may be 350 Mbps and 375 Mbps. Next, packets (which may bethe same or different form the packets transmitted using TxBF) in thequeue are transmitted without using TxBF (and, in some embodiments,there may or may not be a sounding interval), and the estimatedthroughput may be 425 Mbps. Finally, packets in the queue aretransmitted using TxBF with a sounding interval of 200 ms, and theestimated throughput may be 500 Mbps. Based on these measurements, thesounding interval of 200 ms may have the 1^(st) rank position. Thesemeasurements may be repeated multiple times so that frequencies of therank positions can be determined. Next, using the frequencies, themoment may be determined, which is then used to determine the newsounding interval.

Thus, not all the options (sounding intervals, with and without TxBF)may be used. Moreover, the decision regarding the best sounding intervalmay be jointly determined for TxBF and without TxBF. Furthermore, theresulting new sounding interval may be for TxBF or without TxBFdepending on which one opportunistically maximizes the throughput andmaximizes the sounding interval.

In these ways, the electronic device may dynamically determine asounding interval that represents an optimal tradeoff between overheadand the signal-to-noise ratio. Moreover, the electronic device may beable to adapt to changes in the wireless environment, thereby providingimproved communication performance.

We now describe embodiments of an electronic device, which may performat least some of the operations in the communication technique. FIG. 6presents a block diagram illustrating an electronic device 600 inaccordance with some embodiments. This electronic device includesprocessing subsystem 610, memory subsystem 612, and networking subsystem614. Processing subsystem 610 includes one or more devices configured toperform computational operations. For example, processing subsystem 610can include one or more microprocessors, ASICs, microcontrollers,programmable-logic devices, and/or one or more digital signal processors(DSPs).

Memory subsystem 612 includes one or more devices for storing dataand/or instructions for processing subsystem 610 and networkingsubsystem 614. For example, memory subsystem 612 can include dynamicrandom access memory (DRAM), static random access memory (SRAM), and/orother types of memory. In some embodiments, instructions for processingsubsystem 610 in memory subsystem 612 include: one or more programmodules or sets of instructions (such as program module 622 or operatingsystem 624), which may be executed by processing subsystem 610. Notethat the one or more computer programs may constitute a computer-programmechanism. Moreover, instructions in the various modules in memorysubsystem 612 may be implemented in: a high-level procedural language,an object-oriented programming language, and/or in an assembly ormachine language. Furthermore, the programming language may be compiledor interpreted, e.g., configurable or configured (which may be usedinterchangeably in this discussion), to be executed by processingsubsystem 610.

Networking subsystem 614 includes one or more devices configured tocouple to and communicate on a wired and/or wireless network (i.e., toperform network operations), including: control logic 616, an interfacecircuit 618 and one or more antennas 620 (or antenna elements). (WhileFIG. 6 includes one or more antennas 620, in some embodiments electronicdevice 600 includes one or more nodes, such as nodes 608, e.g., a pad,which can be coupled to the one or more antennas 620. Thus, electronicdevice 600 may or may not include the one or more antennas 620.) Forexample, networking subsystem 614 can include a Bluetooth™ networkingsystem, a cellular networking system (e.g., a 3G/4G network such asUMTS, LTE, etc.), a universal serial bus (USB) networking system, anetworking system based on the standards described in IEEE 802.11 (e.g.,a Wi-Fi® networking system), an Ethernet networking system, and/oranother networking system.

In some embodiments, a transmit or receives antenna radiation pattern orantenna pattern of electronic device 600 may be adapted or changed usingpattern shapers (such as reflectors) in one or more antennas 620 (orantenna elements), which can be independently and selectivelyelectrically coupled to ground to steer the transmit antenna radiationpattern in different directions. Thus, if one or more antennas 620includes N antenna-radiation-pattern shapers, the one or more antennas620 may have 2^(N) different antenna-radiation-pattern configurations.More generally, a given antenna radiation pattern may include amplitudesand/or phases of signals that specify a direction of the main or primarylobe of the given antenna radiation pattern, as well as so-called‘exclusion regions’ or ‘exclusion zones’ (which are sometimes referredto as ‘notches’ or ‘nulls’). Note that an exclusion zone of the givenantenna radiation pattern includes a low-intensity region of the givenantenna radiation pattern. While the intensity is not necessarily zeroin the exclusion zone, it may be below a threshold, such as 3 dB orlower than the peak gain of the given antenna radiation pattern. Thus,the given antenna radiation pattern may include a local maximum (e.g., aprimary beam) that directs gain in the direction of an electronic devicethat is of interest, and one or more local minima that reduce gain inthe direction of other electronic devices that are not of interest. Inthis way, the given antenna radiation pattern may be selected so thatcommunication that is undesirable (such as with the other electronicdevices) is avoided to reduce or eliminate adverse effects, such asinterference or crosstalk.

Networking subsystem 614 includes processors, controllers,radios/antennas, sockets/plugs, and/or other devices used for couplingto, communicating on, and handling data and events for each supportednetworking system. Note that mechanisms used for coupling to,communicating on, and handling data and events on the network for eachnetwork system are sometimes collectively referred to as a ‘networkinterface’ for the network system. Moreover, in some embodiments a‘network’ or a ‘connection’ between the electronic devices does not yetexist. Therefore, electronic device 600 may use the mechanisms innetworking subsystem 614 for performing simple wireless communicationbetween the electronic devices, e.g., transmitting advertising or beaconframes and/or scanning for advertising frames transmitted by otherelectronic devices as described previously.

Within electronic device 600, processing subsystem 610, memory subsystem612, and networking subsystem 614 are coupled together using bus 628.Bus 628 may include an electrical, optical, and/or electro-opticalconnection that the subsystems can use to communicate commands and dataamong one another. Although only one bus 628 is shown for clarity,different embodiments can include a different number or configuration ofelectrical, optical, and/or electro-optical connections among thesubsystems.

In some embodiments, electronic device 600 includes a display subsystem626 for displaying information on a display.

Electronic device 600 can be (or can be included in) any electronicdevice with at least one network interface. For example, electronicdevice 600 can be (or can be included in): a desktop computer, a laptopcomputer, a subnotebook/netbook, a server, a tablet computer, asmartphone, a cellular telephone, a smartwatch, a consumer-electronicdevice, a portable computing device, an access point, a transceiver, arouter, a switch, communication equipment, an access point, acontroller, test equipment, and/or another electronic device.

Although specific components are used to describe electronic device 600,in alternative embodiments, different components and/or subsystems maybe present in electronic device 600. For example, electronic device 600may include one or more additional processing subsystems, memorysubsystems, networking subsystems, and/or display subsystems.Additionally, one or more of the subsystems may not be present inelectronic device 600. Moreover, in some embodiments, electronic device600 may include one or more additional subsystems that are not shown inFIG. 6. Also, although separate subsystems are shown in FIG. 6, in someembodiments some or all of a given subsystem or component can beintegrated into one or more of the other subsystems or component(s) inelectronic device 600. For example, in some embodiments program module622 is included in operating system 624 and/or control logic 616 isincluded in interface circuit 618.

While the preceding discussion used particular communication protocolsas illustrative examples, in other embodiments a wide variety ofcommunication protocols and, more generally, wireless communicationtechniques may be used. Thus, the communication technique may be used ina variety of network interfaces. Furthermore, while some of theoperations in the preceding embodiments were implemented in hardware orsoftware, in general the operations in the preceding embodiments can beimplemented in a wide variety of configurations and architectures.Therefore, some or all of the operations in the preceding embodimentsmay be performed in hardware, in software or both. For example, at leastsome of the operations in the communication technique may be implementedusing program module 622, operating system 624 (such as a driver forinterface circuit 618) or in firmware in interface circuit 618.Alternatively or additionally, at least some of the operations in thecommunication technique may be implemented in a physical layer, such ashardware in interface circuit 618.

In the preceding description, we refer to ‘some embodiments.’ Note that‘some embodiments’ describes a subset of all of the possibleembodiments, but does not always specify the same subset of embodiments.

The foregoing description is intended to enable any person skilled inthe art to make and use the disclosure, and is provided in the contextof a particular application and its requirements. Moreover, theforegoing descriptions of embodiments of the present disclosure havebeen presented for purposes of illustration and description only. Theyare not intended to be exhaustive or to limit the present disclosure tothe forms disclosed. Accordingly, many modifications and variations willbe apparent to practitioners skilled in the art, and the generalprinciples defined herein may be applied to other embodiments andapplications without departing from the spirit and scope of the presentdisclosure. Additionally, the discussion of the preceding embodiments isnot intended to limit the present disclosure. Thus, the presentdisclosure is not intended to be limited to the embodiments shown, butis to be accorded the widest scope consistent with the principles andfeatures disclosed herein.

What is claimed is:
 1. An electronic device, comprising: an interfacecircuit configured to communicate with at least another electronicdevice, wherein the electronic device is configured to: initialize a setof potential sounding intervals, wherein a given potential soundinginterval specifies how often transmission beamforming is updated usingsounding packets; communicate, for at least the other electronic device,first packets with and second packets without transmission beamformingfor the set of potential sounding intervals, wherein an antenna patternof the electronic device for use when communicating the first packets isupdated; receiving transmission statistics for communication with atleast the other electronic device; calculate rank positions for the setof potential sounding intervals based at least in part on a performancemetric and numbers of packets transmitted with transmission beamformingfor the set of potential sounding intervals out of a total number ofpackets transmitted; determining an output sounding interval based atleast in part on the calculated rank positions; repeat thecommunicating, receiving, calculating and determining until aconvergence criterion is achieved; calculate frequencies, over multipleiterations, based at least in part on the rank positions for the set ofpotential sounding intervals; determine, when the convergence criterionis achieved, a moment based at least in part on the calculatedfrequencies; revising the set of potential sounding intervals; andrepeat, one or more times, the communicating, receiving, calculating,determining the output sounding interval, calculating the frequencies,and determining the moment based at least in part on the revised set ofpotential sounding intervals.
 2. The electronic device of claim 1,wherein the moment comprises one of: a mean, and a median.
 3. Theelectronic device of claim 1, wherein the electronic device isconfigured to exclude errors in the transmission statistics that areassociated with effects other than transmission beamforming.
 4. Theelectronic device of claim 1, wherein the transmission statisticscomprise one or more of: transmission errors associated with noise,transmission errors associated with collisions and interference, andtransmission errors associated with the antenna pattern.
 5. Theelectronic device of claim 1, wherein the transmission statisticscomprise at least two of: the total number of packets transmitted, thenumber of packets transmitted using transmission beamforming, and anumber of packets transmitted without using transmission beamforming. 6.The electronic device of claim 1, wherein the electronic devicecomprises an antenna with multiple elements that, during thecommunication, provides the antenna pattern.
 7. The electronic device ofclaim 1, wherein the electronic device comprises one of: an accesspoint, and a cellular telephone.
 8. The electronic device of claim 1,wherein the communication of the first packets and the second packets iscompatible with an IEEE 802.11 standard.
 9. A non-transitorycomputer-readable storage medium for use in conjunction with anelectronic device, the computer-readable storage medium storing programinstructions, wherein, when executed by the electronic device, theprogram instructions cause the electronic device to determine a soundinginterval by performing one or more operations comprising: initializing aset of potential sounding intervals, wherein a given potential soundinginterval specifies how often transmission beamforming is updated usingsounding packets; communicating, for at least another electronic device,first packets with and second packets without transmission beamformingfor the set of potential sounding intervals, wherein, during thecommunication, an antenna pattern of the electronic device for use whencommunicating the first packets is updated; receiving transmissionstatistics for communication with at least the other electronic device;calculating rank positions for the set of potential sounding intervalsbased at least in part on a performance metric and numbers of packetstransmitted with transmission beamforming for the set of potentialsounding intervals out of a total number of packets transmitted;determining an output sounding interval based at least in part on thecalculated rank positions; repeating the communicating, receiving,calculating, calculating and determining until a convergence criterionis achieved; calculating frequencies, over multiple iterations, based atleast in part on the rank positions for the set of potential soundingintervals; determining, when the convergence criterion is achieved, amoment based at least in part on the calculated frequencies; revisingthe set of potential sounding intervals; and repeating, one or moretimes, the communicating, receiving, calculating, determining the outputsounding interval, calculating the frequencies, and determining themoment based at least in part on the revised set of potential soundingintervals.
 10. The computer-readable storage medium of claim 9, whereinthe moment comprises one of: a mean, and a median.
 11. Thecomputer-readable storage medium of claim 9, wherein the one or moreoperations comprise excluding errors in the transmission statistics thatare associated with effects other than transmission beamforming.
 12. Thecomputer-readable storage medium of claim 9, wherein the transmissionstatistics comprise one or more of: transmission errors associated withnoise, transmission errors associated with collisions and interference,and transmission errors associated with the antenna pattern.
 13. Thecomputer-readable storage medium of claim 9, wherein the transmissionstatistics comprise at least two of: the total number of packetstransmitted, the number of packets transmitted using transmissionbeamforming, and a number of packets transmitted without usingtransmission beamforming.
 14. The computer-readable storage medium ofclaim 9, wherein the electronic device comprises one of: an accesspoint, and a cellular telephone.
 15. A method for determining a soundinginterval, wherein the method comprises: by an electronic device:initializing a set of potential sounding intervals, wherein a givenpotential sounding interval specifies how often transmission beamformingis updated using sounding packets; communicating, for at least anotherelectronic device, first packets with and second packets withouttransmission beamforming for the set of potential sounding intervals,wherein, during the communication, an antenna pattern of the electronicdevice for use when communicating the first packets is updated;receiving transmission statistics for communication with at least theother electronic device; calculating rank positions for the set ofpotential sounding intervals based at least in part on a performancemetric and numbers of packets transmitted with transmission beamformingfor the set of potential sounding intervals out of a total number ofpackets transmitted; determining an output sounding interval based atleast in part on the calculated rank positions; repeating thecommunicating, receiving, calculating, and determining until aconvergence criterion is achieved; calculating frequencies, overmultiple iterations, based at least in part on the rank positions forthe set of potential sounding intervals; determining, when theconvergence criterion is achieved, a moment based at least in part onthe calculated frequencies; revising the set of potential soundingintervals; and repeating, one or more times, the communicating,receiving, calculating, determining the output sounding interval,calculating the frequencies, and determining the moment based at leastin part on the revised set of potential sounding intervals.
 16. Themethod of claim 15, wherein the moment comprises one of: a mean, and amedian.
 17. The method of claim 15, wherein the method further comprisesexcluding errors in the transmission statistics that are associated witheffects other than transmission beamforming.
 18. The method of claim 15,wherein the transmission statistics comprise one or more of:transmission errors associated with noise, transmission errorsassociated with collisions and interference, and transmission errorsassociated with the antenna pattern.
 19. The method of claim 15, whereinthe transmission statistics comprise at least two of: the total numberof packets transmitted, the number of packets transmitted usingtransmission beamforming, and a number of packets transmitted withoutusing transmission beamforming.
 20. The method of claim 15, wherein theelectronic device comprises one of: an access point, and a cellulartelephone.